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%I #9 Jun 27 2012 13:51:37
%S 0,1,3,2,8,7,5,4,6,22,21,18,17,20,13,12,10,9,11,15,14,19,16,64,63,59,
%T 58,62,50,49,46,45,48,55,54,61,57,36,35,32,31,34,27,26,24,23,25,29,28,
%U 33,30,41,40,38,37,39,52,51,60,56,43,42,47,44,53,196,195,190,189,194
%N Permutation of natural numbers induced by Catalan Automorphism *A074684 acting on the parenthesizations encoded by A014486/A063171.
%C This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184.
%C This is a rare example of a simply defined Catalan Automorphism where the cycle count sequence (A089411) is not monotone. (See A127296 for a much more complex example.)
%H A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme function implementing this automorphism on list-structures/S-expressions:)
%o (define (*A074684! s) (cond ((pair? s) (*A074680! s) (*A074684! (car s)) (*A074684! (cdr s)))) s)
%Y Row 17 of A122201. Inverse of A074683. a(n) = A057163(A074681(A057163(n))).
%Y The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in subpermutations limited by A014137 and A014138 are given by A089411, A086586 and A089412.
%K nonn
%O 0,3
%A _Antti Karttunen_, Sep 11 2002
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